Use double integral in polar coordinates to find the area of the portion of the paraboloid 2z=x² +y² that lies in the cylinder x² + y² = 4

Q: tegral by transforming to polar coordinates.

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Q: Convert the integral to polar coordinates.

A: Polar coordinates Option B

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: 1+√/1-4y² 1-√√/1-4y² _1 = ƒ/³ f²+ √² √²/ y dx dy.

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Q: Use the change in variables s = x + 4y, t = y to find the area of the ellipse x^2 + 8xy + 17y^2,…

A: We have to find the area of the ellipse  x2+8xy+17y2≤1. Use the change in variables s=x+4y and t=y…

Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: Calculate the total length of the circle r = 9 sin(0) as an integral in polar coordinates.

A: r= 9 sin θ [Given] Differentiating both sides w.r.t x we get  r' = 9 cos θ [ ∵ d/dx  (sin t) = cos t…

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: 6) Convert the integral to polar coordinates and evaluate xydx dy y

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Q: Example: Find the surface area of the curve described by x = t³, y = t², 0<t<1, rotated about the…

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Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3